Research On Order Weighted Average Operator Based Multiple Attribute Decision Making Methods

Multiple Attribute Decision Making (MDAM), one of the most important subjects of decision-making science, is widely used in many fields, such as, investment decision making, item evaluation, optimization alternatives, plant site selection, resource assignment, bidding, and comprehensive evaluation on economic benefit, etc. It is of great significance to study the theories and methodologies of MDAM. In the recent 30 years, people have been greatly devoted to the research of MDAM problems, and have been making fruitful achievements. However, the application and research of MDAM methodologies are still far from mature, and still facing new challenges, especially for the research of MDAM methodologies.In this paper, the order weighted average (OWA) operator is applied to the MDAM problems, and new ideas and decision making methods are proposed as a result of the deep research of the pure linguistic MDAM problem. The main contribution of this paper lies in three aspects as below.First, the author expands the order weighted average (OWA) operator from Yager and proposes a Hybrid Order Weighted Geometric Average (HOWGA) operator. This operator integrates both the advantages of the AWA operator and the WGA operator, and combines the importance of both the data itself and the position it stands. Thus it is more reliable in practical situations. After that, some attributes of this operator are provided, and a new MDAM method is introduced based on HOWGA. In this paper, the HOWGA method is compared with the OWA method, and the result shows that the HOWGA method can apparently highlight the project whose attributes are largely deviated. On the other hand, the OWA method can not achieve this goal while assembling the same data. Thus, the HOWGA method can distinguish the projects with defect attributes, and it is more reliable in practical situations. Second, the pure linguistic MDAM problem, of which decision-maker's weights, attribute weights, and attribute values all provided in languages, is deeply studied. The calculating rules of the "a+bi" style connection number and the corresponding "connection number combined order weighted average" (COWA) operator are defined. Also, a new method of pure linguistic MDAM method whose decision makers' weights, attribute weights, and attribute values all provided in languages is introduced. Finally, it is applied in a real case. The analysis of the case reveals that the stable and the instable sectors of the fuzzy linguistic evaluation is perfectly dealt with by using connection numbers, and this method combines the importance of both the data itself and the position it stands, also, it can annihilate the decision maker's inequitable evaluation values, thus avoid the unreasonable decision result.Third, regarding the fuzzy MDAM problem of which the values of attributes and the weights are fuzzy language, the connection number is applied to deal with the fuzzy factors, and the concept of vector's project is expatiated. Furthermore, the concept of the a+bi type connection numbers' module and the cosine of the angle between two connection numbers are proposed, and finally, the concept of connection number's project is proposed. Based on the concepts above, an improved TOPSIS method based on the connection numbers is introduced, using the traditional TOPSIS thinking. Based on a practical case, the new TOPSIS method can assemble much more comprehensive information for decision making, thus the result is more reliable. Additionally, it not only makes the calculation of fuzzy factors much easier, but also avoids the sorting problems relating to the fuzzy sets.Finally, the summarization is presented and some problems are mentioned. The prospect of the MDAM is pointed out.